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Recently, the use of multiplex assays has transformed the goal of group testing from detecting a single disease to diagnosing multiple infections simultaneously. Existing research on multiple\u2010infection group testing data either exclude individual covariate information or ignore possible retests on suspicious individuals. To incorporate both, we propose a new regression model. This new model allows us to perform a regression analysis for each infection using multiple\u2010infection group testing data. Furthermore, we introduce an efficient variable selection method to reveal truly relevant risk factors for each disease. Our methodology also allows for the estimation of the assay sensitivity and specificity when they are unknown. 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